As for me, with pupils messing around with various brass and woodwind instruments,
I only need 3 things 95% of the time:

1. A mouthpiece puller
2. A small screwdriver
3. Patience

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IMO whenever in a pupil / student to teacher / tutor relationship PATIENCE is the most important of these three. A seized mechanism screw on a woodwind is a curse for any tech! In my experience, most of these screws are inferior as also are most small screw drivers.

There are some nice Opto Cable Live Cameras (don´t know the real name . . .)
that come at a reasonable prize. With them you can see everything inside
the horn (red rot, lumps of solder, old shewing gum, things you don´t want to see . . .)

They´re of course not for free, but if you plan to make this a part time living
you could save up for one . . .

Dutch rush is a common name for any of several species of Equisetum (horsetail). Historically, dried pieces were used for scouring pans and such, but if you've not been blessed with an overabundance of the exceedingly invasive nuisance in your garden, you can buy small packets of the stuff from good woodwind shops. It contains a lot of silicates, and does a pretty good job of cleaning a pan or smoothing a reed.